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Problem 9 (Algebra Problem)

Find all solutions of

Solution
There are different ways for a^b to be 1. They are

• when the exponent b is zero
• when the base a is 1
• when the base a is -1 and the exponent b is an even integer

(a) If we set the exponent to zero, we get the two roots -2, and 3

(b) If we set the base to +1, we get two more roots -1 and 2

(c) If we set the base to -1, we get the two roots 0 and 1, both of which result in the exponent being an even integer and thus the final result is 1.

Hence, we have found the roots of -2, -1, 0, 1, 2, and 3. You can check each of these values. It would be interesting to graph the function on the left-hand side of the given equation.

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Last modified on Tuesday, January 12, 1999